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(B) The radioactive decay process is given by $A \longrightarrow B \longrightarrow C 	ext{ (stable)}$.Initially,at $t=0$,the number of atoms of $B$ i

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(B) The radioactive decay process is given by $A \longrightarrow B \longrightarrow C 	ext{ (stable)}$.Initially,at $t=0$,the number of atoms of $B$ is $0$. As $A$ decays,the number of atoms of $B$ starts increasing.The rate of change of the number of atoms of $B$ is given by $\frac{dN_B}{dt} = \lambda_A N_A - \lambda_B N_B$.Initially,$\frac{dN_B}{dt} > 0$,so the number of atoms of $B$ increases. It reaches a maximum value when the rate of formation of $B$ equals the rate of decay of $B$ (i.e.,$\lambda_A N_A = \lambda_B N_B$).After reaching this maximum,the number of atoms of $B$ starts decreasing as the supply from $A$ diminishes. Since both the growth and decay processes are governed by exponential functions,the graph will show a smooth rise to a maximum followed by an exponential decay. Among the given options,the graph in image $981-b1026$ correctly represents this behavior.

$A$ sample of a radioactive nucleus $A$ disintegrates to another radioactive nucleus $B$,which in turn disintegrates to some other stable nucleus $C$. Plot a graph showing the variation of the number of atoms of nucleus $B$ versus time:
(Assume that at $t=0$,there are no $B$ atoms in the sample)

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$A$ sample of a radioactive nucleus $A$ disintegrates to another radioactive nucleus $B$,which in turn disintegrates to some other stable nucleus $C$. Plot a graph showing the variation of the number of atoms of nucleus $B$ versus time:(Assume that at $t=0$,there are no $B$ atoms in the sample)